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Relevant bibliographies by topics / Arrondi Stochastique

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Academic literature on the topic 'Arrondi Stochastique'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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Journal articles on the topic "Arrondi Stochastique"

1

Tynda, Aleksandr, Samad Noeiaghdam, and Denis Sidorov. "Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind." Bulletin of Irkutsk State University. Series Mathematics 39 (2022): 62–79. http://dx.doi.org/10.26516/1997-7670.2022.39.62.

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The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gausstype quadrature formula is used to approximate integrals during the discretization of the proposed projection method. The estimate of accuracy of approximate solution is obtained. Stochastic arithmetics is also used based on the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. Applying this approach it is possible to f

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Noeiaghdam, Samad, and Sanda Micula. "A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel." Mathematics 9, no. 17 (2021): 2172. http://dx.doi.org/10.3390/math9172172.

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Load leveling problems and energy storage systems can be modeled in the form of Volterra integral equations (VIE) with a discontinuous kernel. The Lagrange–collocation method is applied for solving the problem. Proving a theorem, we discuss the precision of the method. To control the accuracy, we apply the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library. For this aim, we apply discrete stochastic mathematics (DSA). Using this method, we can control the number of iterations, errors a

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3

Noeiaghdam, Samad, Aliona Dreglea, Jihuan He, et al. "Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library." Symmetry 12, no. 10 (2020): 1730. http://dx.doi.org/10.3390/sym12101730.

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This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estima

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Noeiaghdam, L., S. Noeiaghdam, and D. N. Sidorov. "Dynamical control on the Adomian decomposition method for solving shallow water wave equation." iPolytech Journal 25, no. 5 (2021): 623–32. http://dx.doi.org/10.21285/1814-3520-2021-5-623-632.

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The aim of this study is to apply a novel technique to control the accuracy and error of the Adomian decomposition method (ADM) for solving nonlinear shallow water wave equation. The ADM is among semi-analytical and powerful methods for solving many mathematical and engineering problems. We apply the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method which is based on stochastic arithmetic (SA). Also instead of applying mathematical packages we use the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. In this library we will write all codes

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5

Noeiaghdam, Samad, and Mohammad Ali Fariborzi Araghi. "A Novel Algorithm to Evaluate Definite Integrals by the Gauss-Legendre Integration Rule Based on the Stochastic Arithmetic: Application in the Model of Osmosis System." Mathematical Modelling of Engineering Problems 7, no. 4 (2020): 577–86. http://dx.doi.org/10.18280/mmep.070410.

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Finding the optimal iteration of Gaussian quadrature rule is one of the important problems in the computational methods. In this study, we apply the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library to find the optimal iteration and optimal approximation of the Gauss-Legendre integration rule (G-LIR). A theorem is proved to show the validation of the presented method based on the concept of the common significant digits. Applying this method, an improper integral in the solution of th

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Araghi, Mohammad Ali Fariborzi, and Samad Noeiaghdam. "A Valid Scheme to Evaluate Fuzzy Definite Integrals by Applying the CADNA Library." International Journal of Fuzzy System Applications 6, no. 4 (2017): 1–20. http://dx.doi.org/10.4018/ijfsa.2017100101.

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The aim of this paper is to estimate the value of a fuzzy integral and to find the optimal step size and nodes via the stochastic arithmetic. For this purpose, the fuzzy Romberg integration rule is considered as an integration rule, then the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method is applied which is a method to describe the discrete stochastic arithmetic. Also, in order to implement this method, the CADNA (Control of Accuracy and Debugging for Numerical Applications) is applied which is a library to perform the CESTAC method automatically. A theorem is prov

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7

Asserrhine, Jalil, Jean-Marie Chesneaux, and Jean-Luc Lamotte. "Estimation of Round-off Errors on Several Computers Architectures." JUCS - Journal of Universal Computer Science 1, no. (7) (1995): 454–68. https://doi.org/10.3217/jucs-001-07-0454.

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Numerical validation of computed results in scientific computation is always an essential problem as well on sequential architecture as on parallel architecture. The probabilistic approach is the only one that allows to estimate the round-off error propagation of the floating point arithmetic on computers. We begin by recalling the basics of the CESTAC method (Controle et Estimation Stochastique des Arrondis de Calculs). Then, the use of the CADNA software (Control of Accuracy and Debugging For Numerical Applications) is presented for numerical validation on sequential architecture. On paralle

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8

Noeiaghdam, Samad, Sanda Micula, and Juan J. Nieto. "A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library." Mathematics 9, no. 12 (2021): 1321. http://dx.doi.org/10.3390/math9121321.

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In this paper, a nonlinear fractional order model of COVID-19 is approximated. For this aim, at first we apply the Caputo–Fabrizio fractional derivative to model the usual form of the phenomenon. In order to show the existence of a solution, the Banach fixed point theorem and the Picard–Lindelof approach are used. Additionally, the stability analysis is discussed using the fixed point theorem. The model is approximated based on Indian data and using the homotopy analysis transform method (HATM), which is among the most famous, flexible and applicable semi-analytical methods. After that, the CE

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Noeiaghdam, Samad, Denis Sidorov, Alyona Zamyshlyaeva, Aleksandr Tynda, and Aliona Dreglea. "A Valid Dynamical Control on the Reverse Osmosis System Using the CESTAC Method." Mathematics 9, no. 1 (2020): 48. http://dx.doi.org/10.3390/math9010048.

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The aim of this study is to present a novel method to find the optimal solution of the reverse osmosis (RO) system. We apply the Sinc integration rule with single exponential (SE) and double exponential (DE) decays to find the approximate solution of the RO. Moreover, we introduce the stochastic arithmetic (SA), the CESTAC method (Controle et Estimation Stochastique des Arrondis de Calculs) and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library instead of the mathematical methods based on the floating point arithmetic (FPA). Applying this technique, we would be ab

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10

Noeiaghdam, Samad, Denis Sidorov, Abdul-Majid Wazwaz, Nikolai Sidorov, and Valery Sizikov. "The Numerical Validation of the Adomian Decomposition Method for Solving Volterra Integral Equation with Discontinuous Kernels Using the CESTAC Method." Mathematics 9, no. 3 (2021): 260. http://dx.doi.org/10.3390/math9030260.

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The aim of this paper is to present a new method and the tool to validate the numerical results of the Volterra integral equation with discontinuous kernels in linear and non-linear forms obtained from the Adomian decomposition method. Because of disadvantages of the traditional absolute error to show the accuracy of the mathematical methods which is based on the floating point arithmetic, we apply the stochastic arithmetic and new condition to study the efficiency of the method which is based on two successive approximations. Thus the CESTAC method (Controle et Estimation Stochastique des Arr

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Dissertations / Theses on the topic "Arrondi Stochastique"

1

El, Arar El-Mehdi. "Stochastic models for the evaluation of numerical errors." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG104.

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L'idée de considérer les erreurs d'arrondi comme des variables aléatoires n'est pas nouvelle. Basées sur des outils tels que l'indépendance des variables aléatoires ou le théorème central limite, plusieurs propositions ont démontré des bornes d'erreur en O(√n). Cette thèse est dédiée à l'étude de l'arrondi stochastique (SR) en tant que remplaçant du mode d'arrondi déterministe par défaut. Tout d'abord, nous introduisons une nouvelle approche pour dériver une borne probabiliste de l'erreur en O(√n), basée sur le calcul de la variance et l'inégalité de Bienaymé-Chebyshev. Ensuite, nous développo

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2

Chotin-Avot, Roselyne. "Architectures matérielles pour l'arithmétique stochastique discrète." Paris 6, 2003. http://hal.upmc.fr/tel-01267458.

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